Final answer:
There cannot be both one-one and onto mappings from set A to set B since set A has fewer elements. Only one-one (injective) mappings are possible, with the number of such mappings being 6×5×4×3×2, which equals 720. Therefore, the correct option is (d) 720.
Step-by-step explanation:
If set A contains 5 elements and set B contains 6 elements, the number of both one-one (injective) and onto (surjective) mappings from A to B cannot exist because A has fewer elements than B, and therefore a onto function is not possible. However, if we are looking just for the number of one-one mappings (also known as injective functions) from A to B, we can calculate this as follows:
- Select an element from set A to map to an element in set B. There are 6 choices.
- For the next element in set A, there are 5 choices left in set B (since one was already used and it needs to be a one-one function).
- Continue this process until all elements in set A are mapped, reducing the number of choices in set B by one each time.
The total number of injective mappings is the product of these choices: 6 × 5 × 4 × 3 × 2, which equals 720. Thus, the correct option is (d) 720. It is important to mention the correct option in the final answer and choose any one option that accurately represents the solution to the problem presented.